The goal of silicate is to bridge planar geospatial data types with flexible mesh data structures and visualization.

We aim to provide

- a
*common-form*for representing hierarchical data structures - a
*universal converter*between complex data types - topological primitives for analysis and exploration.

The core of silicate are *worker functions* that are generic and work with any kind of data that has hierarchical structure. These functions work on *models*, that include various formats (sf, sp, trip) and also on silicate models themselves.

We have the following worker verbs, designed to work with many spatial data formats and with silicate’s own structures.

`sc_object()`

- highest level properties, the “features”`sc_coord()`

- all instances of coordinates, labelled by vertex if the source model includes them`sc_vertex()`

- only unique coordinates (in some geometric space)`sc_path()`

- individual paths, sequential traces`sc_edge()`

- unique binary relations, unordered segments (segments and edges are currently under review, and may change)`sc_segment()`

- all instances of edges`sc_arc()`

- unique topological paths, arcs either meet two other arcs at a node, or include no nodes`sc_node()`

- unique nodes

The idea is that each function can return the underlying entities of a data object, no matter its underlying format. This interoperability design contrasts with major spatial packages that require format peculiarities in order to work, even when these details are not relevant.

Silicate defines a number of key models to represent various interpretations of hierarchical (usually spatial) data. These are `SC`

, `PATH`

, `ARC`

and `TRI`

. Most models have a counterpart *structurally-optimized* version with a similar name: `SC0`

, `PATH0`

, `TRI0`

. Other models are possible, and include `DEL`

in the in-development anglr package that extends `TRI`

.

Each model is composed of a type of *primitive*, and each provides a normalization (de-duplication) of geometry for efficiency and or topology. Silicate quite deliberately separates the concepts of geometry and topology completely. Primitives define the topology (edges, paths, arcs, or triangles) and the vertex table defines the geometry. We reserve the names `x_`

, `y_`

, `t_`

(time) and `z_`

(elevation) for the usual geometric dimensions, and these are treated specially by default. No limit is put geometric dimension however, it’s possible to store anything at all on the vertex table. Some models include an `object`

table, and this represents a higher level grouping of primitives (and corresponds to *features* in SF).

The most general model is `SC`

, composed of three tables `vertex`

, `edge`

and `object`

and all entities are explicitly labelled. Indexes between tables are unique and persistent and arbitrary, they can be arbitrarily accessed. This is closely related to the more bare-bones `SC0`

model, composed of only two tables `vertices`

, and `objects`

. These are related *structurally* by nesting the relations within the object table. Here the relations are not persistent, so we can subset the objects but we cannot change the vertex table with updating these indexes.

`SC0`

can deal with 0-dimensional topology types (points) as well as 1-dimensional types (edges), but `SC`

is strictly for edges.

Further models `PATH`

, `ARC`

, and `TRI`

cover a broad range of complex types, and each is fundamental and distinct from the others. `SC`

can be used to represent any model, but other models provide a better match to specific use-cases, intermediate forms and serve to expand the relationships between the model types.

`SC`

is the universal model, composed of binary relationships, edges defined by pairs of vertices (a structural primitive model)`TRI`

also a structural primitive model, for triangulations`PATH`

a sequential model, for the standard spatial vector types, shapes defined by*paths*`ARC`

a sequential model, for*arc-node topology*a shared-boundary decomposition of path models`SC0`

is a stripped down structural model analogous to`SC`

, there are only implicit relations of object to vertices, with a nested list of edge indexes

The models `PATH0`

and `ARC0`

are in-development. By analogy to `SC0`

they will be composed of two tables, `object`

and `vertex`

with nested structural-index tables on `object`

holding the path and arc indexes that are row numbers of `vertex`

. It’s not clear yet if this vertex table should be de-duplicated.

Earlier versions included a mix of these models, and the definitions have changed many times. Still a work-in-progress.

An extension of the `TRI`

model `DEL`

is provided in anglr which builds *high-quality* triangulations, but the structural representation is the same.

Each model is created by using a set of generic verbs that extract the underlying elements of a given model. This design means that the models themselves are completely generic, and methods for worker verbs can be defined as needed for a given context. Our ideal situation would be for external packages to publish methods for these verbs, keeping package-specific code in the original package. We think this provides a very powerful and general mechanism for a family of consistent packages.

There is another important function `unjoin()`

use to normalize tables that have redundant information. The `unjoin()`

isthe opposite of the database join, and has a nearly identical counterpart in the dm package with its `decompose_table()`

. Unjoin is the same as `tidyr::nest()`

but returns two tables rather than splitting one into the rows of other.

The `unjoin`

is a bit out of place here, but it’s a key step when building these models, used to remove duplication at various levels. It’s the primary mechanism for *defining and building-in* topology, which is precisely the relationships between entities in a model. This function is published in the CRAN package unjoin.

Silicate is not about simple features, it’s about transcending those limitations for day to day data problems. Unfortunately we inevitably have to couch this work in that context.

Modern geospatial science needs normal-form data structures.

Modern GIS standards generally represent spatial data as nested lists, whether in accordance with the Simple Features (SF) standard of the Open Geospatial Consortium, or in `geojson`

format. Most commonly used geometric libraries are based on one or both of these two standards. We argue that (1) the agreed representations in modern GIS geometry effectively restrict ongoing development of GIS as a whole, and (2) the enforced representation of geometry as nested lists as a central form is inefficient.

SF does not address what “non-simple” features are or might be, yet clearly these include important application domains such as GPS data, transport networks, point clouds, computer aided design, virtual and/or augmented reality, and 3D games. Each of these significant arenas have their own standards which are difficult to reconcile or unite without risking fragmentation and inefficiency.

SF and nested-list representations are limited because:

- Shapes are not represented as topological primitives and so internal boundaries are precluded.
- Shapes are represented as paths so only planar polygonal shapes are possible.
- Shapes may exist in XY[Z[M]] geometry, but this is not extensible, with no capacity to store data against component geometry elements.
- Shapes have no persistent naming of features or their components.
- There is no capacity for internal topology of shapes or within collections (no vertex-, edge-, or path-sharing).

These limitations mean that SF cannot fully represent every-day data forms from tracked objects, transport, Lidar, 3D models, statistical graphics, topological spatial maps, TopoJSON, CAD drawings, meshes or triangulations. Translations between geospatial forms and the grammars of data science can be disjointed, relying on localized implementations that are lossy or inefficient, require third party workflows, or involve unnecessary tasks.

GIS applications generally diverge from common standards in different ways but none currently provide a normal-form model. There is no standard way to normalize data by detecting and removing redundancy (topology), or to densify data (a common necessity in planning domains). There is no standard way to extend the types although complex forms are well established in other domains.

The common “well-known” formats of encoding geometry (WKB/WKT for binary/text) represent (pre-)aggregated data, yet the input levels of aggregation are often not directly relevant to desired or desirable levels of aggregation for analysis. A key stage in many GIS analyses is thus an initial disaggregation to some kind of atomic form followed by re-aggregation.

We propose a common form for spatial data that is inherently disaggregated, that allows for maximally-efficient on-demand re-aggregation (arbitrarily re-composable hierarchies), and that covers the complexity of geometric and topological types widely used in data science and modelling. We provide tools in R for more general representations of spatial primitives and the intermediate forms required for translation and analytical tasks. These forms are conceptually independent of R itself and are readily implemented with standard tabular data structures.

There is not one single normal form that should always be used. There is one universal form that every other model may be expressed in, but also other forms that are better suited or more efficient for certain domains. We show that conversion between these forms is more straightforward and extensible than from SF or related types, but is also readily translated to and from standard types. The most important forms we have identified are “universal” (edges and nodes), “2D primitives” (triangles), “arcs” (shared boundaries), and “paths” (normalized forms of SF types).

```
# Install the development version from GitHub:
# install.packages("devtools")
devtools::install_github("hypertidy/silicate")
```

Convert a known external model to a silicate model.

```
library(silicate)
#>
#> Attaching package: 'silicate'
#> The following object is masked from 'package:stats':
#>
#> filter
x <- SC(minimal_mesh) ## convert simple features to universal form
y <- ARC(minimal_mesh) ## convert simple features to "arc-node" form
```

Obtain the elements of a known model type.

```
sc_vertex(x)
#> # A tibble: 14 x 3
#> x_ y_ vertex_
#> <dbl> <dbl> <chr>
#> 1 0 0 zF3v3e
#> 2 0 1 4u503v
#> 3 0.2 0.2 PCZKVr
#> 4 0.2 0.4 yRREbL
#> 5 0.3 0.6 Gzi5J5
#> 6 0.5 0.2 tTSvR9
#> 7 0.5 0.4 Nbm44D
#> 8 0.5 0.7 i7zK6P
#> 9 0.69 0 dw198X
#> 10 0.75 1 2Jngno
#> 11 0.8 0.6 KzDKqp
#> 12 1 0.8 bq6mA9
#> 13 1.1 0.63 yXuzBG
#> 14 1.23 0.3 AMPmcu
sc_edge(x)
#> # A tibble: 15 x 3
#> .vx0 .vx1 edge_
#> <chr> <chr> <chr>
#> 1 zF3v3e 4u503v UNLZfF
#> 2 4u503v 2Jngno Jqlzdw
#> 3 2Jngno bq6mA9 0mzDPM
#> 4 i7zK6P bq6mA9 qa8zB8
#> 5 i7zK6P KzDKqp NYn6eI
#> 6 dw198X KzDKqp CIU725
#> 7 zF3v3e dw198X 15Qy7K
#> 8 PCZKVr tTSvR9 oQOuH4
#> 9 tTSvR9 Nbm44D PHX0xl
#> 10 Gzi5J5 Nbm44D YqMUyt
#> 11 yRREbL Gzi5J5 mhZJuV
#> 12 PCZKVr yRREbL 48OFjO
#> 13 KzDKqp yXuzBG 0wjfSR
#> 14 yXuzBG AMPmcu ltsAl6
#> 15 dw198X AMPmcu KgGydZ
sc_node(y)
#> # A tibble: 2 x 1
#> vertex_
#> <chr>
#> 1 hz0DjH
#> 2 RxFNq8
sc_arc(y)
#> # A tibble: 4 x 2
#> arc_ ncoords_
#> <chr> <int>
#> 1 kj1gA8 6
#> 2 KwmoDy 7
#> 3 MNRJOs 4
#> 4 oZnlbW 2
```

There are two kinds of models, *primitive* and *sequential*.

Primitive-based models are composed of *atomic* elements that may be worked with arbitrarily, by identity and grouping alone.

Sequential-based models are bound to ordering and contextual assumptions. We provide the `PATH`

and `ARC`

models as generic, relational forms that provide a convenient intermediate between external forms and primitives models. Further intermediate models exist, including monotone and convex decompositions of polygons.

There is one universal primitives-based model, an edge-only model with two tables at its core. Higher level structures are described by grouping tables, with as many levels as required. Any other model can be expressed in this form.

We also differentiate *structural primitives*, which are specializations that are more convenient or more efficient in certain cases. These include triangulations (2D primitives), and segment structures (1D primitives), and could provide higher dimensional forms (3D primitives, etc. ).

Currently, we provide support for the universal model `SC`

, the sequential models `PATH`

(simple features belongs here, amongst many others) and `ARC`

(arc-node topology, TopoJSON-like, OpenStreetMap), and structural primitives `TRI`

.

In practice a segment model is trivial to generate, “SEG” but we haven’t done that. This would be analogous to the format used by `rgl::rgl.lines`

or `spatstat::psp`

.

We take care to allow for *labelling* (identity) of component elements, without taking full responsibility for maintaining them. Random IDs are created as needed, but any operation that works with existing IDs should be stable with them.

The spacebucket (arbitrary multi-layer polygonal overlays) and sphier (generic hierarchies from atomic forms) show two different approaches to the problem of hierarchical data and flexible representations.

The key difference between the silicate approach and simple features is the separation of geometry and topology. This allows for normalization (de-duplication) of the entities that are present or that can be identitied. Simple features has no capacity to de-duplicate or otherwise identify vertices, edges, paths or arcs, though tools that work with simple features do construct these schemes routinely in order to perform operations. When these richer, topological structures are built they are usually then discarded and the vertices are again de-normalized and again expressed explicitly without recording any of the relationships. In this sense, simple features can be described as an *explicitly-stored PATH analogue*, and is no different from the model used by shapefiles, binary blobs in databases, and many other spatial vector formats. There are a number of notable exceptions to this including TopoJSON, Eonfusion, PostGIS, QGIS geometry generators, Fledermaus, Mapbox, WebGL, Threejs, D3, AFrame, Lavavu but unfortunately there’s no overall scheme that can unify these richer structures.

The silicate family is composed of a small number of packages that apply the principles here, either to read from path forms or primitive forms. As work continues some of these will be incorporated into the silicate core, when that is possible without requiring heavy external dependencies.

Looking for a music reference? I always am: Child’s Play, by Carcass.

Please note that the ‘silicate’ project is released with a Contributor Code of Conduct. By contributing to this project, you agree to abide by its terms.